Note: If you have run this command in the past, you probably want to purge your chain storage, so that you run through this tutorial with a clean slate. You can do this easily by using docker-compose rm to delete your existing docker volume.
You should start to see blocks being produced by your node in your terminal.
You can interact with your node using the Polkadot UI:
Note: You will need to use a Chromium based browser (Google Chrome) to have this site interact with your local node. The Polkadot UI is hosted on a secure server, and your local node is not, which may cause compatibility issues on Firefox. The other option is to clone and run the Polkadot UI locally. (The Brave Browser has also been causing compatibility issues).
To point the UI to your local node, you need to adjust the Settings. Just select 'Local Node (127.0.0.1:9944)' from the endpoint dropdown:
Click on the chain name > Development node/endpoint to connect to > Local Node (127.0.0.1:9944) > Switch
If you go into the Explorer tab of the UI, you should also see blocks being produced!